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Simplifying 4.9t2 + -1.6249t + -0.78 = 0 Reorder the terms: -0.78 + -1.6249t + 4.9t2 = 0 Solving -0.78 + -1.6249t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.1591836735 + -0.3316122449t + t2 = 0 Move the constant term to the right: Add '0.1591836735' to each side of the equation. -0.1591836735 + -0.3316122449t + 0.1591836735 + t2 = 0 + 0.1591836735 Reorder the terms: -0.1591836735 + 0.1591836735 + -0.3316122449t + t2 = 0 + 0.1591836735 Combine like terms: -0.1591836735 + 0.1591836735 = 0.0000000000 0.0000000000 + -0.3316122449t + t2 = 0 + 0.1591836735 -0.3316122449t + t2 = 0 + 0.1591836735 Combine like terms: 0 + 0.1591836735 = 0.1591836735 -0.3316122449t + t2 = 0.1591836735 The t term is -0.3316122449t. Take half its coefficient (-0.1658061225). Square it (0.02749167026) and add it to both sides. Add '0.02749167026' to each side of the equation. -0.3316122449t + 0.02749167026 + t2 = 0.1591836735 + 0.02749167026 Reorder the terms: 0.02749167026 + -0.3316122449t + t2 = 0.1591836735 + 0.02749167026 Combine like terms: 0.1591836735 + 0.02749167026 = 0.18667534376 0.02749167026 + -0.3316122449t + t2 = 0.18667534376 Factor a perfect square on the left side: (t + -0.1658061225)(t + -0.1658061225) = 0.18667534376 Calculate the square root of the right side: 0.432059422 Break this problem into two subproblems by setting (t + -0.1658061225) equal to 0.432059422 and -0.432059422.Subproblem 1
t + -0.1658061225 = 0.432059422 Simplifying t + -0.1658061225 = 0.432059422 Reorder the terms: -0.1658061225 + t = 0.432059422 Solving -0.1658061225 + t = 0.432059422 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1658061225' to each side of the equation. -0.1658061225 + 0.1658061225 + t = 0.432059422 + 0.1658061225 Combine like terms: -0.1658061225 + 0.1658061225 = 0.0000000000 0.0000000000 + t = 0.432059422 + 0.1658061225 t = 0.432059422 + 0.1658061225 Combine like terms: 0.432059422 + 0.1658061225 = 0.5978655445 t = 0.5978655445 Simplifying t = 0.5978655445Subproblem 2
t + -0.1658061225 = -0.432059422 Simplifying t + -0.1658061225 = -0.432059422 Reorder the terms: -0.1658061225 + t = -0.432059422 Solving -0.1658061225 + t = -0.432059422 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1658061225' to each side of the equation. -0.1658061225 + 0.1658061225 + t = -0.432059422 + 0.1658061225 Combine like terms: -0.1658061225 + 0.1658061225 = 0.0000000000 0.0000000000 + t = -0.432059422 + 0.1658061225 t = -0.432059422 + 0.1658061225 Combine like terms: -0.432059422 + 0.1658061225 = -0.2662532995 t = -0.2662532995 Simplifying t = -0.2662532995Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.5978655445, -0.2662532995}
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